Educational device for teaching simple and complex mathematical concepts

ABSTRACT

An educational device comprising a holder or axle ( 2 ) for a plurality of side by side revolvable arms ( 3 ) or counters whereby in use the arms revolve by twirling the holder or by manipulating arms so that when placed on a support surface some arms lie on the left hand side of the holder while the remaining arms lie on the right hand side of the holder. The device consists of arms which revolve on a handle ( 1 ). It can be manipulated in a number of ways and adapts both to play and to serious educational purpose. In broad educational mode the device is an exploration tool and toy where children can develop skills and play invented games or invent their own. In its main educational use, the device is a mathematics exploration tool and toy; is of a construction which makes it compatible with the decimal system of number among others; and in particular provides a visual-kinaesthetic method for the teaching/learning/understanding/exploration of mathematics.

TECHNICAL FIELD

[0001] This invention relates to an educational device. In particular,this invention relates to an educational device enabling the teaching ofsimple and complex mathematical concepts and operations to childrenusing random and planned combinations of numbers and operations.

BACKGROUND ART

[0002] Many teaching aids for children's education are known and usedaround the world. For the teaching of mathematics, devices representingnumbers, such as building blocks, rods and abaci are used. However, manysuch devices render it difficult for children to understand manipulationof numbers and basic processes and operations in mathematicsparticularly regarding subtraction, multiplication, division, fractions,decimals, ratios, percentages, place value and number bases, as well asbasic concepts and operations in algebra and geometry.

[0003] It would be desirable to provide an educational device, simple inconstruction and operation, that assists children in learning andunderstanding basic mathematical processes and operations.

[0004] It is an object of the present invention to address the foregoingproblems or at least to provide the public with a useful choice.

[0005] Further aspects and advantages of the present invention willbecome apparent from the ensuing description which is given by way ofexample only.

DISCLOSURE OF INVENTION

[0006] According to one aspect of the present invention there isprovided an education device comprising a holder or axle for a pluralityof side by side revolvable arms whereby in use the arms rotate bytwirling the holder or by manipulating arms so that, when placed on asupport surface, some arms lie on the left hand side of the axle whilethe remaining arms lie on the right hand side of the axle.

[0007] It will be appreciated that the device can be used for variousgames and to develop a variety of cognitive and dexterity skills whilealso being a type of dice and/or abacus. When used as an abacus thedevice shows patterns which can relate to numbers, enabling people tosee or determine relationships in the patterns and between the numbersthey may represent.

[0008] Provision is made for parts to be added to or removed from thedevice to make it an abacus or dice of varying numeric value or pattern,e.g. to be a ‘6-arm abacus’ or an ‘8-arm abacus’ or a ‘dice of 6’ or a‘dice of 10’. Provision is also made for coding of the parts, e.g. byarms of different colour, size, shape or imprint, again to provide abacior dice of varying numeric or visual or spatial pattern.

[0009] In this invention the counters or balls of the traditional abacusbecome arms or counters or balls which are attached to or may be placedon an axle in such a way that they rotate. The shape of the arms orballs or counters is immaterial. Indeed the arms themselves can serve asballs or counters and ‘arms’ is used hereafter to refer to all of these.It will be appreciated that the use of the term ‘arms’ includes anydevice capable of revolving about the axle.

[0010] Arms may be placed, e.g. snapped, on the abacus or removed fromit for a variety of purposes. They may be held in place by a handle atone end of the axle and a stopper or a second handle at the other endand/or by containing or guiding devices dispersed on the axle.

[0011] Arms may be without special markings or may be marked ordistinguished or coded to denote numerical values such as 5 or 10 orcomposite values such as 5×3 or 6−2. The information which an armreveals may have different significance according to imprint,instructions or rules, e.g. depending on whether the arm lies to theleft of the axle or to the right (see Best Modes below regarding use ofthe device of the present invention). The information may be an integralpart of the arm or affixed to it or to the axle, e.g. by a sticker.

[0012] In this invention the endings of the axle of the device may bedesigned to fit the one with the other so that any number of the devicesmay be joined together and make a new device of more complex structure.The means by which one device is attached to another is immaterial.

[0013] In one preferred form the device is more particularly designed asa play thing associated with games and skills.

[0014] In a second preferred form the device is more particularlydesigned for educational purposes as both a type of abacus and/or dice.That is, it provides means of understanding and operating mathematicalprocesses such as counting, adding, subtracting, multiplying, dividing,working with fractions, decimals, ratios, percentages. In this form andcongruent with the decimal number system it may, for example be providedwith 10 detachable arms each having a value of ‘1’ or such other numberas may be preferred. This format provides for different sizes of diceand abaci according to how many arms are attached during use. Forexample, with 10 arms attached it may be a ‘dice of 10’ or a ‘10-armabacus’ while with 6 arms attached it may be a dice or abacus of 6.

[0015] In a third preferred form the device is more particularlydesigned for play and display purposes in the dark. Its revolving armsmay be luminescent and/or hold bulbs of various colours supplied withelectricity (however generated) and switches. Alternatively, light mayissue from sources in the handle and/or axle. A light display may beprovided using a light source in the holder with optic fibres extendingfrom the source along the hollow rod to the counters.

[0016] Arms may be attached to the axle in a variety of ways. In apreferred form they may be clipped onto and removed from an axle whichmay have means of keeping arms from touching each other. However, anysuitable means for attaching the arms to the axle may be used as long asthe arms are able to revolve about same. The arms may be plain or inornamented form. Ornamentation is not limited to colouring. For example,the arms may be designed to produce noise, music, light. They may becoded, e.g. with numbers to give any desired numerical value to the arm.

[0017] Devices may be provided with a storage bag or an accessory suchas a ‘holster’ or belt which may be attached to the person of the user.Provision is also made for spare arms to be stored separately, as in asmall bag.

BRIEF DESCRIPTION OF DRAWINGS

[0018] Further aspects of the present invention will become apparentfrom the following description which is given by way of example only andwith reference to the accompanying drawings in which:

[0019]FIG. 1 is a side view of a 10-counter device showing ‘3 and 7’ asits abacus or number pattern and ‘3’, the number of counters to theleft, as its dice value.

[0020]FIG. 2 is a side view of a 10-counter device with 4 countersremoved and leaving a ‘6-arm abacus’ with a ‘3 and 3’ number pattern, ora ‘dice of 6’ with a value (left side) of ‘3’.

[0021]FIG. 3 is a side view of a 10-counter device showing an abacuspattern of ‘7 and 3’ and a dice value of ‘7’.

[0022]FIG. 4 shows a side view of a 7-arm play or games device anddetails the design of a clip.

[0023]FIG. 5 is a perspective view of a 7-arm derivation designed forplay, game, and dice use and shows an axle ending 7 and an axle ending 8which would allow two or more of the devices to be joined end to end.

[0024]FIG. 6 shows ‘visual number’ patterns from a 4-arm abacusexemplifying an ‘addition’ or ‘conservation of number’ model, i.e. thepatterns which make four.

[0025]FIG. 7 shows two steps in the use of the device in ‘subtraction’mode, such that in the second step when one arm has been swung to theright (subtracted) three can be seen to be ‘left’, i.e. 4−1=3.

[0026]FIG. 8 shows the device in a sample multiplication/divisionapplication. Specifically, in visual number, it shows that 5×2=10 andthat 10÷2=5.

[0027]FIG. 9 shows diagrams of some shape, space and symmetry patternswith abaci of different size, i.e. relating to ‘geometry’ mode.

[0028]FIG. 10 exemplifies an ‘algebra’ mode with various patterning ofballs of the same and different colour.

[0029]FIG. 11 shows the device in ‘binary numeration’ mode.

[0030]FIG. 12 shows how devices may be joined to increase their range ofuse or specifically shows how children could visually demonstrate theimproper fraction one and 3 quarters.

BEST MODES FOR CARRYING OUT THE INVENTION

[0031] In the drawings moulded handle 1 and rod or axle 2 and optionalsecondary handle 4 provide a framework to support arms 3. Arms 3 arefree to rotate on the rod 2. In FIG. 4 the ball 5 and clip 6 areintegral parts of the moulded arm 3.

[0032] When the device is manipulated in use, the arms 3 can be made torotate in clockwise or anti-clockwise fashion. This becomes the basisfor skills which players can develop. Equally importantly, the devicemay be twirled, so that the arms 3 revolve in a relatively jumbled orrandom way in the air before being brought down upon a flat surface suchas a table or pad or cushion (not shown). Some arms 3 will lie to theleft of the axle 2 and some to the right. The sum of the arms 3 to theleft and right will always equal the total number of arms 3 on thedevice. This forms the basis for many educational applications and for awide variety of games and is a key feature of the abacus.

[0033] An example of educational use is with the learning of basicaddition number facts. For facts which add to four for example, fourarms 3 are placed on the device. This is shown in FIG. 6. By a count ofarms to the left and right of the axle it can be demonstrated that 4+0,3+1, 2+2, 1+3 and 0+4 all equal 4. Children can ‘discover’ all suchpatterns. They can record them, e.g. in stylised drawings. They canwrite them as equations and express them as ‘number stories’. In thisand other examples, children are helped by the clear ‘visual number’patterns which the device provides.

[0034] Another example of educational use is with understandingsubtraction and learning basic subtraction facts. For example, as shownin FIG. 7, when 4 arms are placed first to the left, representing any 4objects, then when one is swung over to the right, 3 are left. Childrenthus make discoveries such that 4−1=3 and make number stories on thisbasis.

[0035] Another example of educational use is with understandingmultiplication and division and learning basic multiplication anddivision number facts. For example, children may make discoveries orengage in operations as in FIG. 8 where they find that 5 twos make 10 orthat 10 can be divided into 5 equal parts.

[0036] Other examples of educational use are in geometry where childrenare helped to explore shape and space. Visual number patterns such asare shown in FIG. 9 may be used with the device in ‘still’ or in‘swinging’ mode to help develop concepts like ‘below, top, middle,bottom, next to, beside; forwards, backwards, over, towards, away from’.They may also explore symmetry by creating or talking about symmetricaland repeating patterns.

[0037] Other examples of educational use are in algebra. Some of theseare shown in FIG. 10. The first two of the 6 diagrams show how patternsmay be made with arm-endings of the same and different colours. Thethird pattern from the top relates conceptually to the division of 10 by4 and shows a quotient of 2 and remainder of 2. The fourth relates tothree 2s plus 1 making 7, or 7 divided into 2s. The fifth provides aschema for building a two-times table, with each of the 10 ‘units’ beingseen by children not as ‘ones’ but as ‘twos’ by focusing on the shape ofthe arms above the ball ending. The last diagram shows how each arm orball may be given a value of say 10, so that the 10-times table is shownor may be derived.

[0038] Another example of educational use is with binary numeration. InFIG. 11 and reading from the right, the arms may be given values of 2⁰,2¹, 2², and so on—equating to 1, 2, 4 and so on in decimal. When thearms are in a downward position, as in the top example, they areconsidered ‘off’ and have only potential numerical value. When rotatedup the arms are ‘on’ and their value is actualised. Thus the middleexample of FIG. 11 has 2 arms ‘on’ and their value is 1+2, i.e. totals3. The lower example has arms ‘on’ to the value (from the right) of0+2+0+0+16+32, i.e. 50. This usage sets children down the path ofdiscovering the binary manner by which computers handle numbers

[0039] Similar and other procedures/models, using the device of thepresent invention, allow other addition, subtraction, multiplication anddivision number facts or combinations to be experienced and learned,likewise work with fractions, decimals, ratios and percentages as wellas applications in geometry, algebra and statistics.

[0040] Mathematical use of the device is not restricted to working witha single device. FIGS. 12 and 13, for example, shows how children mightput 2 four-arm devices together side by side or join them end to end tomake a visual representation of the improper fraction 1 and threequarters.

[0041] It can accordingly be seen, with reference to the attachedself-explanatory drawings, that the educational device of the presentinvention enables opportunities wide ranging in nature. It provides aninnovative means of educating children in many aspect of Number,Algebra, Geometry and Statistics in an enjoyable fulfilling hands-onexploratory manner.

[0042] Aspects of the present invention have been described by way ofexample only and it should be appreciated that modifications andadditions may be made thereto without departing from the scope thereof.

What I claim is:
 1. An educational device comprising a holder or axlefor a plurality of side by side revolvable arms or counters whereby inuse the arms revolve by twirling the holder or by manipulating arms sothat when placed on a support surface some arms lie on the left handside of the holder while the remaining arms lie on the right hand sideof the holder.
 2. The device as claimed in claim 1 wherein the axle ismade decimal system congruent by providing support for up to 10attachable/detachable arms.
 3. The device of claim 1 or claim 2 wherebyin mathematical calculations the value of any one or more of the armssupported on the axle may be varied.
 4. A device as claimed in any oneof claims 1 to 3 wherein any one or more parts thereof may be adapted toemit light such as having incorporated or applied thereon luninescentmaterial or bulbs, optical fibres or LED's in connection with a powersource.
 5. Use of the device of any one of the above claims as a dicewherein the number of arms lying on a named side of the axle, normallythe left side, represents the value of the throw of the dice.
 6. Use ofthe device as claimed in any one of claims 1 to 4 as an abacus whereinany one or more of the plurality of arms supported on the axle may beprovided with varying values, such that when the device lies on asupport surface the left or right position of the arms relative to theaxis and/or the coding of the arms and/or assignation of numericalvalues to the arms provides number patterns which permit a multiplicityof mathematical learning models and operations.
 7. Use of the device asclaimed in any one of claims 1 to 4 as an abacus wherein by means of theending of any one device being able to be attached to the opposite endof any other, an extension of mathematical learning and operationalmodels is provided.
 8. A device substantially as claimed herein in anyone of claims 1 to 4 with reference to any example and/or drawingthereof.
 9. The device as claimed in any of the above claims whereby inlogical or mathematical terms when the device is supported on a surfacethe arms may have binary significance, i.e. each may be considered asswitched on or off according to their position to the left or right ofthe axle or to their upwards/downwards position.
 10. Use of the deviceof the present invention in accordance with claim 5 or claim 6 or claim7 or claim 8 or claim 9 substantially as described herein with referenceto any example and/or drawing thereof.
 11. Any invention as described orclaimed herein.